Social networks have a lifecycle: They start with a small core of early adopters, swell as mainstream users get pulled in by their friends, and then see growth taper off as people get turned off by spam. That's why Friendster is forgotten and why MySpace is looking increasingly stagnant. The price for reaching an audience advertisers care about seems to be a site users can't stand. Facebook, however, isn't following the fashionable trend.

By the numbers, there are no signs of Facebook fatigue. The social network's ranks swelled from 100 million in August to 120 million in October. If it sustains that improbable pace, it will encompass the entire world's population by 2012.

There's a threat to Facebook's dominance — and it's not the one you'd think. Privacy is the bugaboo everyone brings up. The company has launched a new program, Facebook Connect, which links other websites into Facebook's News Feed, the site's tattletale compendium of their friends' online activities. Connect, which is profiled in today's Times, is similar in some ways to Beacon, a feature which outraged privacy activists around this time last year when it revealed Facebook users' holiday purchases. But Beacon proved a short-lived Grinch; Facebook rapidly modified the program, and the protests died down.

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If anything, the complaint users have about Facebook is not that the site shares their private details, but that their so-called friends do. A surfeit of information has led some to cull their friends' lists on the site. That's more than fine with Facebook CEO Mark Zuckerberg, who has always sought to have his site reflect real-world relationships.

Facebook's trust problem isn't with users; it's with the Web publishers and application developers Facebook executives are trying so desperately to court. And this is a serious problem, because they're the people on which Facebook is trying to build a next-generation advertising business.

By developing Facebook apps — if you've thrown a sheep or been bitten by a zombie on Facebook, you'ved used one of these — or signing up with Connect, these companies are essentially advertising on Facebook. They're just doing it subtly, through the News Feed — and sometimes the advertisement is simply for their own service. The medium is new, but the intent is the same as any other advertiser's: To interrupt users and grab their attention.

Which makes Facebook Connect's lack of progress curious. The company has signed up some minor players — among online-video sites, Hulu but not YouTube; for city guides, CitySearch but not Yelp; the San Francisco Chronicle but not The New York Times; and so on. By far the biggest omission, though, are the makers of Facebook apps.

When Facebook allowed outsiders to write applications for its site last year, companies like Slide, RockYou, iLike, and Flixster eagerly signed up; the largest Facebook-app developers raised hundreds of millions of dollars on the promise that they could piggyback on the Facebook phenomenon. But then came the zombies.

Apps which let you, say, bite your friends and turn them into werewolves provided mindless entertainment to some and annoyance to others proliferated; clever developers figured out ways to get users to spam their friends to get them to sign up for the app, too. The abuses proliferated — and Facebook's growth slowed measurably.

So Facebook cracked down on the application developers — unfairly and arbitrarily, some say. iLike, a music app, and Causes, an app which let users spread the word about do-gooding efforts, got special treatment, while other apps were temporarily removed from Facebook for privacy violations or spam. The image problems got so bad that Facebook, to the derision of many, appointed its top flack, Elliot Schrage, to run its platform efforts.

Those same application developers are now telling anyone who asks to take a wait-and-see attitude with Connect. The main attraction of Connect, as with the application platform before it, is placement in Facebook's News Feed. The lesson developers learned with the Facebook platform is that there are no guarantees of placement, and that the rules change too rapidly to build a solid business on it.

That's why Digg, the popular news-discussion website founded by Web 2.0 playboy Kevin Rose, is rumored to have struck a deal with Facebook that guaranteed a level of News Feed placement before it agreed to sign up with Connect. And app developers are advising other potential Facebook partners to get similar guarantees in writing.

It's a dilemma for Facebook. Zuckerberg has avoided the spam problems that doomed Friendster and hobbled MySpace; by cracking down on app developers, he's kept Facebook appealing to its users. But to keep Facebook independent and turn it into a big business, he'll have to build up a big advertising business. And inserting commercial messages into the News Feed is key to that. It's spam by another name, with an invoice attached.

Zuckerberg may be reluctant to make promises to other Connect partners precisely because his advertising salespeople are hoping to charge them for guaranteed placement. CBS, which is airing this year's Victoria's Secret lingerie show on Wednesday, has signed up with Connect, and the network is paying to make sure that people read on Facebook about their friends' plans to tune in to watch Heidi Klum. That's a harbinger of the future.

The application developers and website operators vying for Facebook users' attention might be relieved if Facebook just started explicitly charging for placement. A rate card would be easier to decipher than Facebook's obscure and constantly shifting antispam rules. But will a deluge of sponsored messages turn off users? There's no easy answer. If there were, Mark Zuckerberg might be more than a paper billionaire by now.